<h2>DESCRIPTION</h2>

<em>r.drain</em> traces a flow through a least-cost path in an
elevation model or cost surface. For cost surfaces, a movement
direction map must be specified with the
<b>direction</b> option and the <b>-d</b> flag to trace a flow path following 
the given directions. Such a movement direction map can be generated with 
<em><a href="r.walk.html">r.walk</a></em>, 
<em><a href="r.cost.html">r.cost</a></em>, 
<em><a href="r.slope.aspect.html">r.slope.aspect</a></em> or 
<em><a href="r.watershed.html">r.watershed</a></em>
provided that the direction is in degrees, measured counterclockwise
from east.

<p>
The <b>output</b> raster map will show one or more least-cost paths
between each user-provided location(s) and the minima (low category
values) in the raster <b>input</b> map. If the <b>-d</b> flag is used
the output least-cost paths will be found using the direction raster
map.  By default, the <b>output</b> will be an integer CELL map with
category 1 along the least cost path, and null cells elsewhere.

<p>With the <b>-c</b> (<em>copy</em>) flag, the input raster map cell values are
copied verbatim along the path. With the <b>-a</b> (<em>accumulate</em>)
flag, the accumulated cell value from the starting point up to the current
cell is written on output. With either the <b>-c</b> or the <b>-a</b> flags, the
<b>output</b> map is created with the same cell type as
the <b>input</b> raster map (integer, float or double).  With
the <b>-n</b> (<em>number</em>) flag, the cells are numbered
consecutively from the starting point to the final point.
The <b>-c</b>, <b>-a</b>, and <b>-n</b> flags are mutually
incompatible.

<p>For an elevation surface, the path is calculated by choosing the
steeper "slope" between adjacent cells. The slope calculation
accurately accounts for the variable scale in lat-lon projections. For
a cost surface, the path is calculated by following the movement
direction surface back to the start point given
in <em><a href="r.walk.html">r.walk</a></em> or
<em><a href="r.cost.html">r.cost</a></em>. The path search stops 
as soon as a region border or a neighboring NULL cell is encountered, 
because in these cases the direction can not be determined (the path 
could continue outside the current region).

<p>The <b>start_coordinates</b> parameter consists of map E and N grid coordinates of
a starting point. Each x,y pair is the easting and northing (respectively) of
a starting point from which a least-cost corridor will be developed.
The <b>start_points</b> parameter can take multiple vector maps containing 
additional starting points.
Up to 1024 starting points can be input from a combination of the
<b>start_coordinates</b> and <b>start_points</b> parameters.

<h3>Explanation of output values</h3>

Consider the following example: 

<div class="code"><pre>
Input:                          Output:
  ELEVATION SURFACE               LEAST COST PATH
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 19. 20. 18. 19. 16. 15. 15.    .   .   .   .   .   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 20| 19| 17. 16. 17. 16. 16.    .   . 1 . 1 . 1 .   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 18. 18. 24. 18. 15. 12. 11.    .   .   .   .   . 1 .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 22. 16. 16. 18. 10. 10. 10.    .   .   .   .   . 1 .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 15. 15. 15. 10. 8 . 8 .    .   .   .   .   .   . 1 .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 24. 16. 8 . 7 . 8 . 0 . 12.    .   .   .   .   .   . 1 .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 9 . 8 . 7 . 8 . 6 . 12.    .   .   .   .   .   .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
</pre></div>

<p>
The user-provided starting location in the above example is 
the boxed <b>19</b> in the left-hand map. The path in the output 
shows the least-cost corridor for moving from the starting 
box to the lowest (smallest) possible point. This is the path a raindrop 
would take in this landscape.
<p>
With the <b>-c</b> <em>(copy)</em> flag, you get the following result:

<div class="code"><pre>
Input:                          Output:
  ELEVATION SURFACE               LEAST COST PATH
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 19. 20. 18. 19. 16. 15. 15.    .   .   .   .   .   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 20| 19| 17. 16. 17. 16. 16.    .   . 19. 17. 16.   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 18. 18. 24. 18. 15. 12. 11.    .   .   .   .   . 15.   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 22. 16. 16. 18. 10. 10. 10.    .   .   .   .   . 10.   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 15. 15. 15. 10. 8 . 8 .    .   .   .   .   .   . 8 .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 24. 16. 8 . 7 . 8 . 0 .12 .    .   .   .   .   .   . 0 .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 9 . 8 . 7 . 8 . 6 .12 .    .   .   .   .   .   .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .

Note that the last <em>0</em> will not be put in the null values map.
</pre></div>

<p>
With the <b>-a</b> <em>(accumulate)</em> flag, you get the following result:

<div class="code"><pre>
Input:                          Output:
  ELEVATION SURFACE               LEAST COST PATH
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 19. 20. 18. 19. 16. 15. 15.    .   .   .   .   .   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 20| 19| 17. 16. 17. 16. 16.    .   . 19. 36. 52.   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 18. 18. 24. 18. 15. 12. 11.    .   .   .   .   . 67.   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 22. 16. 16. 18. 10. 10. 10.    .   .   .   .   . 77.   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 15. 15. 15. 10. 8 . 8 .    .   .   .   .   .   . 85.   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 24. 16. 8 . 7 . 8 . 0 .12 .    .   .   .   .   .   . 85.   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 9 . 8 . 7 . 8 . 6 .12 .    .   .   .   .   .   .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
</pre></div>

<p>
With the <b>-n</b> <em>(number)</em> flag, you get the following result:

<div class="code"><pre>
Input:                          Output:
  ELEVATION SURFACE               LEAST COST PATH
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 19. 20. 18. 19. 16. 15. 15.    .   .   .   .   .   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 20| 19| 17. 16. 17. 16. 16.    .   . 1 . 2 . 3 .   .   .   .
. .  ---  . . . . . . . . . .    . . . . . . . . . . . . . . .
. 18. 18. 24. 18. 15. 12. 11.    .   .   .   .   . 4 .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 22. 16. 16. 18. 10. 10. 10.    .   .   .   .   . 5 .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 15. 15. 15. 10. 8 . 8 .    .   .   .   .   .   . 6 .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 24. 16. 8 . 7 . 8 . 0 .12 .    .   .   .   .   .   . 7 .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
. 17. 9 . 8 . 7 . 8 . 6 .12 .    .   .   .   .   .   .   .   .
. . . . . . . . . . . . . . .    . . . . . . . . . . . . . . .
</pre></div>

With the <b>-d</b> <em>(direction)</em> flag, the direction raster is used 
for the input, rather than the elevation surface. The output is then created 
according to one of the <b>-can</b> flags.
<div class="code"><pre>
The directions are recorded as degrees CCW from East:
       112.5     67.5         i.e. a cell with the value 135 
157.5  135   90  45   22.5    means the next cell is to the North-West 
       180   x   0            
202.5  225  270  315  337.5
       247.5     292.5
</pre></div>

<h2>NOTES</h2>

If no direction input map is given, <em>r.drain</em> currently finds
only the lowest point (the cell having the smallest category value) in
the input file that can be reached through directly adjacent cells
that are less than or equal in value to the cell reached immediately
prior to it; therefore, it will not necessarily reach the lowest point
in the input file. It currently finds <em>pits</em> in the data,
rather than the lowest point in the entire input
map. The <em><a href="r.fill.dir.html">r.fill.dir</a></em>,
<em><a href="r.terraflow.html">r.terraflow</a></em>,
and <em><a href="r.basins.fill.html">r.basins.fill</a></em> modules
can be used to fill in subbasins prior to processing
with <em>r.drain</em>.

<p>
<em>r.drain</em> will not give sane results at the region boundary. On outer rows
and columns bordering the edge of the region, the flow direction is always directly out 
of the map. In this case, the user could try adjusting the region extents slightly with 
<em>g.region</em> to allow additional outlet paths for <em>r.drain</em>.

<h2>EXAMPLES</h2>

<h3>Path to the lowest point</h3>

In this example we compute drainage paths from two given points
following decreasing elevation values to the lowest point.
We are using the full North Carolina sample dataset.
First we create the two points from a text file using
<em><a href="v.in.ascii.html">v.in.ascii</a></em> module
(here the text file is CSV and we are using unix here-file syntax
with EOF, in GUI just enter the values directly for the parameter input):

<div class="code"><pre>
v.in.ascii input=- output=start format=point separator=comma &lt;&lt;EOF
638667.15686275,220610.29411765
638610.78431373,220223.03921569
EOF
</pre></div>

Now we compute the drainage path:

<div class="code"><pre>
r.drain input=elev_lid792_1m output=drain_path drain=drain start_points=start
</pre></div>

Before we visualize the result, we set a color table for the elevation
we are using and we create a shaded relief map:

<div class="code"><pre>
r.colors map=elev_lid792_1m color=elevation
r.relief input=elev_lid792_1m output=relief
</pre></div>

Finally we visualize all the input and output data:

<div class="code"><pre>
d.shade shade=relief color=elev_lid792_1m
d.vect map=drain_path color=0:0:61 width=4 legend_label="drainage paths"
d.vect map=start color=none fill_color=224:0:0 icon=basic/circle size=15 legend_label=origins
d.legend.vect -b
</pre></div>

<div align="center">
<a href="r_drain.png"><img src="r_drain.png" alt="drainage using r.watershed" width="300" height="280"></a>
<br>
<i>Figure: Drainage paths from two points flowing into the points with
lowest values</i>
</div>

<h3>Path following directions</h3>

To continue flow even after it hits a depression, we need to supply a
direction raster map which will tell the <em>r.drain</em> module how to
continue from the depression. To get these directions, we use the
<em><a href="r.watershed.html">r.watershed</a></em> module:

<div class="code"><pre>
r.watershed elevation=elev_lid792_1m accumulation=accum drainage=drain_dir
</pre></div>

The directions are categorical and we convert them to degrees using
raster algebra:

<div class="code"><pre>
r.mapcalc "drain_deg = if(drain_dir != 0, 45. * abs(drain_dir), null())"
</pre></div>

Together with directions, we need to provide the <em>r.drain</em> module
with cost values. We don't have any cost to assign to specific cells,
so we create a constant surface:

<div class="code"><pre>
r.mapcalc "const1 = 1"
</pre></div>

Now we are ready to compute the drainage paths.
We are using the two points from the previous example.

<div class="code"><pre>
r.drain -d input=const1 direction=drain_deg output=drain_path_2 drain=drain_2 start_points=start
</pre></div>

We visualize the result in the same way as in the previous example.

<div align="center">
<a href="r_drain_with_r_watershed_direction.png"><img src="r_drain_with_r_watershed_direction.png" alt="drainage using r.watershed" width="300" height="280"></a>
<br>
<i>Figure: Drainage paths from two points where directions from
r.watershed were used</i>
</div>

<h2>KNOWN ISSUES</h2>

<p>Sometimes, when the differences among integer cell category values in the
<em><a href="r.cost.html">r.cost</a></em> cumulative cost surface output are 
small, this cumulative cost output cannot accurately be used as input to
<em>r.drain</em> (<em>r.drain</em> will output bad results).
This problem can be circumvented by making the differences
between cell category values in the cumulative cost output bigger. It
is recommended that if the output from <em>r.cost</em> is to be used
as input to <em>r.drain</em>, the user multiply the <em>r.cost</em>
input cost surface map by the value of the map's cell resolution,
before running <em>r.cost</em>. This can be done using
<em><a href="r.mapcalc.html">r.mapcalc</a></em>. The map resolution can be
found using <em><a href="g.region.html">g.region</a></em>.
This problem doesn't arise with floating point maps.


<h2>SEE ALSO</h2>

<em>
<a href="g.region.html">g.region</a>,
<a href="r.cost.html">r.cost</a>,
<a href="r.fill.dir.html">r.fill.dir</a>,
<a href="r.basins.fill.html">r.basins.fill</a>,
<a href="r.watershed.html">r.watershed</a>,
<a href="r.terraflow.html">r.terraflow</a>,
<a href="r.mapcalc.html">r.mapcalc</a>,
<a href="r.walk.html">r.walk</a>
</em>

<h2>AUTHORS</h2>

Completely rewritten by Roger S. Miller, 2001<br>
July 2004 at WebValley 2004, error checking and vector points added by
Matteo Franchi (Liceo Leonardo Da Vinci, Trento) and
Roberto Flor (ITC-irst, Trento, Italy)

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